1. Find `3 1/2 - 1 3/4`
Solution:
`=3 (1)/(2) - 1 (3)/(4)`
Method-1: Solution by separating whole parts and fraction parts
`=3(1)/(2)- 1(3)/(4)`
Combine whole parts and fraction parts together
`=(3 - 1)+((1)/(2)-(3)/(4))`
`=2+((1)/(2)-(3)/(4))`
Here, LCM of 2 and 4 is 4. Convert each fractions into like fractions. So multiply numerator and denominator by the ratio of LCM and denominator of the fraction
`=2+(1xx2)/(2xx2)-(3xx1)/(4xx1)`
`=2+(2)/(4)-(3)/(4)`
`=2+(2 - 3)/(4)`
`=2+(-1)/(4)`
`=1+1+(-1)/(4)`
`=1+(1+(-1)/(4))`
`=1 3/4`
2. Find `2 3/4 - 1 5/6`
Solution:
`=2 (3)/(4) - 1 (5)/(6)`
Method-1: Solution by separating whole parts and fraction parts
`=2(3)/(4)- 1(5)/(6)`
Combine whole parts and fraction parts together
`=(2 - 1)+((3)/(4)-(5)/(6))`
`=1+((3)/(4)-(5)/(6))`
Here, LCM of 4 and 6 is 12. Convert each fractions into like fractions. So multiply numerator and denominator by the ratio of LCM and denominator of the fraction
`=1+(3xx3)/(4xx3)-(5xx2)/(6xx2)`
`=1+(9)/(12)-(10)/(12)`
`=1+(9 - 10)/(12)`
`=1+(-1)/(12)`
`=0+1+(-1)/(12)`
`=0+(1+(-1)/(12))`
`=11/12`
3. Find `2 3/4 - 1 1/4`
Solution:
`=2 (3)/(4) - 1 (1)/(4)`
Method-1: Solution by separating whole parts and fraction parts
`=2(3)/(4)- 1(1)/(4)`
Combine whole parts and fraction parts together
`=(2 - 1)+((3)/(4)-(1)/(4))`
`=1+((3)/(4)-(1)/(4))`
`=1+(2)/(4)`
`=1+(1)/(2)`
`=1 1/2`
4. Find `2 1/4 - 3/4`
Solution:
`=2 (1)/(4) - (3)/(4)`
Method-1: Solution by separating whole parts and fraction parts
`=2(1)/(4)- 0(3)/(4)`
Combine whole parts and fraction parts together
`=(2 - 0)+((1)/(4)-(3)/(4))`
`=2+((1)/(4)-(3)/(4))`
`=2+(-2)/(4)`
`=2+(-1)/(2)`
`=1+1+(-1)/(2)`
`=1+(1+(-1)/(2))`
`=1 1/2`
This material is intended as a summary. Use your textbook for detail explanation.
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